I don't understand the whole Mad Hatter/Alice thing

It depends on the adaptation. Most of the もっと見る modern adaptations have Alice as もっと見る of an adult (at least 18, but I've seen adaptations where she's in her late 20s).

I think the fact that they originally disliked each other is one of the reasons a romantic connection between them became so popular. That's the new "thing" for characters -- the もっと見る antagonistic they are, the もっと見る interesting and 人気 that relationship becomes.